no8 Appendix VL flanges for the bolts. The left flange has a spherical projection K, which fits within two half-discs j fastened to the right flange, and the pivot L bears against the shaft G. Also there are steel bushes in the left flange to receive the barrel-shaped ends of the bolts, which are a loose fit radially. When the axes of the shafts deviate slightly a movement takes place at the surfaces K and L, which movement is freely permitted on account of the clearances at M and N and the sliding of the bolts in the steel bushes. At the same time it must be noticed that either tension or compres- sion in an axial direction is fully resisted, and the whole coupling is not large in diameter. The remaining coupling was used by Dr. Hopkinson for coupling dynamos, and is only adaptable to rather small torques. Its construction is very similar to Brother- hood's, having a hollow casting R keyed to the shaft p, and a disc s keyed to the shaft Q. These are connected by a leather disc T held down to casting and disc by the ring washers u u, and all the metal surfaces are rounded where they meet the bending portion of the leather. This coupling has proved very useful for its purpose. P. 526. Bpicyclic Trains. Example 78. Two spur wheejs, A and B, whose diameters are 2 and 3 respectively, are in gear with an annular wheel C whose diameter is 8. The wheels A and C have a common axis, but B is carried by an arm centred on the axis of A. (i). If A makes 5 rotations while c makes one, both in the same direction, find the angle described by the arm during the time. (2). Let C make 3 rotations in the opposite direction to the 5 Fig. 974*.